Sumários
Some important distributions of continuous random variables: the Exponential, Gama and Chi-Square distributions
24 Novembro 2014, 13:30 • Graça Leão Fernandes
Some important distributions of continuous random variables:
Exponential:
- The relation between the Poisson and the Exponential distributions;
- Probability density and cumulative distribution functions;
- Moment generating function, mean and variance;
- Lack of memory;
- theorem of aditivity
Gama:
- The relation between the Exponential and Gamma distributions;
- Probability density and cumulative distribution functions;
- Moment generating function, mean and variance;
- theorem of aditivity
Chi-Square distribution:
- The relation between the Gamma and chi-Square distributions;
- Probability density and cumulative distribution functions;
- Moment generating function, mean and variance;
- theorem of aditivity
Some important distributions of discrete random variables: Uniform, Bernoulli, binomial and Poisson
21 Novembro 2014, 15:30 • Graça Leão Fernandes
Resolution of the following exercises:
Book- nºs: 5.72, 5.75, 5.77, 5.80, 5.81.
Exercises for chapter 4- nºs: 11, 13, 16, 17
Some important distributions of discrete random variables:Uniform discrete, Bernoulli and Binomial.
14 Novembro 2014, 15:30 • Graça Leão Fernandes
Resolution of the 3rd mini test.
Solving exercises:
From Book- ch.5 - nºs: 5.1, 5.40, 5.44, 5.50
From Exercises for Ch.4 - nºs: 1, 2, 3, 5
Bernoulli, Binomial and Poisson distribution
11 Novembro 2014, 13:30 • Graça Leão Fernandes
Bernoulli, Binomial distributions: examples and problem solving
Poisson distribution:
- Definition;
- Assumptions of a Poisson Process;
- Probability and cumulative probability functions;
- Moment generating function, mean and variance;
- Aditivity theorem.
Theoretical quastion nº 3
Some important discrete distributions: uniform discrete, Bernoulli and Binomial
10 Novembro 2014, 13:30 • Graça Leão Fernandes
Some important discrete distributions:
- Uniform discrete at n points
- Definition;
- Probability function;
- Momente generating function, espected value and variance.
- Bernoulli
- Definition of a Bernoulli random trial;
- Probability function;
- Momente generating function, espected value and variance.
- Binomial
- Definition from a successive Bernoulli random trials;
- Probability function;
- Momente generating function, espected value and variance;
- The distibution of the number of failures;
- The aditivity theorem;
- Use of tables and calculators to compute probabilities.